■ GDC is allowed ■for SL and HL studentsA slice of bread is modelled by a two-dimensional shape consisting of a rectangle with the graph of \(y = 1 - {x^2},\; - 1 \le x \le 1\) on top of the rectangle, as shown in the figure. The line segment AC (dashed) has endpoints \({\rm{A}}\left( { - 1,\; - 1} \right)\) and \({\rm{C}}\left( {c,\;1 - {c^2}} \right)\). Show that if AC divides the shape into two regions of equal area then the value of c is the one real number solution to the cubic equation \({c^3} + 3{c^2} + 6c - 6 = 0\).